[seqfan] Re: No progress on the classic "Football pools" problem in 52 years

[Benoît Jubin]

It looks like A004044(0) = 1 !
In that case, the trivial lower bound is attained.  Actually, in the known
cases where 3^n/(2n+1) is an integer, then that lower bound is attained.
This means that there is a solution with no overlaps.  If this is true in
general, this is probably well-known by people knowing Hamming codes (of
which I am not).  Or did I misinterpret the problem ?
Best regards,
Benoît

On Mon, Jun 21, 2021 at 6:52 AM Neil Sloane <njasloane at gmail.com> wrote:

> I grew up in a country where many people played the football pools every
> week (trying to guess the winners of next week's games: you know Manchester
> United is going to beat Arsenal, but there are 13 games to predict).
>
> The classical problem translates into finding the smallest covering code in
> {0,1,2}^n with covering radius 1.  The sequence (A004044) begins
> 1,3,5,9,27, but even after 52 years, a(6) is still not known.  Tonight I
> came across a lot of references, which I have added to A004044.  a(6) is
> known to be 71, 72, or 73.
> If you can solve it, you might not make any money, but you will probably
> get your name in the science section of the newspaper.
>
> Good publicity for the OEIS too!
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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